Nathan Mull: Gödel’s Theorems and Anti-Functionalism

Monday, January 14
12:30-1:20pm
JCL 346
Gödel’s Theorems and Anti-Functionalism

This is an announcement for the Pizza Seminar, a grad student initiative
where PhD students present to each other over a free lunch. Talks can be
a chance to present something from your research of general interest,
practice a conference presentation, or just tell us about something
interesting.

The talk will take place in JCL 346 on Monday, January 14. We have
another philosophically-minded talk this week, presented by Nathan Mull (@nmull).

Gödel’s Theorems and Anti-Functionalism
Are all true mathematical theorems provable? Is the mind just a
computer? It turns out that there is an interesting connection between
these two questions. I will give a high-level overview of Gödel’s
Incompleteness theorems and how philosophers have used them to try to
prove that the mind transcends the capabilities of a computer.

I wanted to share this before but forgot. The same day @nmull gave this talk, ACM TechNews shared this article: https://www.nature.com/articles/d41586-019-00083-3

Machine Learning Leads Mathematicians to Unsolvable Problem
Nature
Davide Castelvecchi
January 8, 2019

In exploring a machine learning problem, a team of researchers at the Technion-Israel Institute of Technology in Haifa discovered a mathematically unanswerable question associated with logical paradoxes defined by mathematician Kurt Godel. The team determined “learnability”—whether an algorithm can extract a pattern from limited data—is connected to Godel’s continuum hypothesis, in which a statement can be neither validated nor invalidated via standard mathematical language. This determination stemmed from an investigation into the link between learnability and “compression,” which entails finding a way of abstracting the salient features of a large dataset in a smaller dataset. The team described learnability as the ability to make predictions about a large dataset by sampling a small number of data points. Although the validation of the continuum hypothesis means a small sample is sufficient to make the extrapolation, its invalidation means no finite sample can ever be sufficient.

Full Article